Data and code from: Network theory predicts ecosystem robustness across environmental conditions

Network theory quantifies how changes in species richness, S, lead to changes in the number of interactions (or links) between species, L. Networks with a steep relationship between L and S have a high number of links per species, making the network resistant to collapse and therefore more robust. However, changes in S often coincide with environmental shifts, which can lead to impacts on L that are not expected from network theory. In this paper, we constructed relationships between L and S for 18 ecosystems using 1081 observations collected across 420 environmental conditions. We found that environmental noise (unspecified spatiotemporal variation) and environmental gradients (directional environmental change) commonly affected ecological network size (S and L), community composition, and also induced network rewiring, which means that species changed interaction partners as the environment changed. Yet, we found the log(L) ~ log(S) relationship to be remarkably constant across environmental conditions. Specifically, the slope of this relationship remained constant across conditions, implying consistency in how species loss proportionally affects L. Our results therefore show that network theory predicts ecosystem robustness across environmental conditions. These results suggest generality to how environmental drivers operate at the level of ecological networks, which is encouraging for conservation.

Methods
We searched the literature to collect ecological network datasets with at least eight observations per ecosystem (to allow for meaningful linear regressions), ensuring that these datasets were based on field observations rather than simulations. Network observations were coded as undirected adjacency matrices, where 0 and 1 indicated the absence or presence of an interaction, respectively. For each network observation, we recorded the number of species (S), the number of interactions (or links, L), and the composition of observed species and links. In cases where organisms were not identified at the species level, the term "species" referred to taxa.